Hands-On Math Activities for Middle School ~ The Organized Homeschooler | Math

Hands-On Math Activities for Middle School ~ The Organized Homeschooler

Hands-on activities can make middle school math much easier! Use these activities and interactive notebooks to learn topics such as algebra, geometry, and number sense. #middleschool #math #homeschool

MATHEMATIC HISTORY

Mathematics is one of the oldest sciences in human history. In ancient times, Mathematics was defined as the science of numbers and shapes. Mathematics, like other branches of science, has evolved as time passes; it’s no longer possible to describe it in a few sentences. What I have to express now is going to be words that emphasize its various aspects, rather than describe mathematics. In taking care of, mathematics is a skill like painting and music. The great majority of mathematicians perform it as an art. Using this point of view, the fact that a work done, a developed theory works in one of the ways or another other than mathematics doesn’t concern them much. What matters in their mind may be the depth of the task done, the novelty of the strategy used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the objective of science could be the universe; If it is to know, rule and direct everything in the universe, we must have the ability to browse the book of nature. The book of nature is written in the language of mathematics, with the highly cited words of Galile; its letters are shapes of geometry. To be able to understand and interpret them, we must know the language of mathematics. In another aspect, mathematics is definitely an intellectual game like chess.

Some mathematicians also notice it as a game. Mathematics is only a tool for the user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics is currently far beyond the dimensions any human can rule. Therefore, I do not think that people who handle mathematics are more than we understand and perceive it from mathematics compared to the blind touched net understands and perceives the elephant. The term mathematics, for initially, BC. It absolutely was utilized by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It had been in the 380s. The term meaning is “what must be learned”, that’s, information. In the years before these dates, as opposed to the word mathematics, words that mean geometry, equal to it in geometry or old languages ​​were used.

It’s difficult to say anything definite about where and how mathematics started. When we take documents that are not based on archaeological findings that want interpretation, but open enough to require interpretation, We are able to say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics were only available in Egypt. As you know, 97% of the Egyptian lands aren’t suitable for agriculture; It’s the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, at the end of the floods due to the Nile river every year, the boundaries of the landowners’lands become obscure. Considering that the landowners also pay taxes in proportion to the land they own, after each flood, the “geometricists” of the state, that are responsible for these works, should arrive at take the mandatory measurements and supply the landowners just as much land as they had in the last year. Herodotus says that geometry has begun to emerge consequently of those measurements and calculations. A second opinion about the birth of mathematics is the main one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics came to be in Egypt. Nonetheless it came to be from the boredom of clergymen and priests, not the necessity for measurement-calculation brought on by Nile floods. At that time, the sole intellectual class of countries such as for example Egypt was the priest class. Since the livelihood with this class is provided by people or their state, they’ve much time to give to intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that time, in the same way others invented games like chess, bridge, and go&hellip ;.Both of these views might be true; priests desired to simplify the job of the geometric, or they discovered just how to calculate the aspects of some geometric shapes such as triangular and trapezoidal to check that the distribution was fair, and this way resulted in the birth of geometry.

We shall divide the written history of mathematics into five periods. The initial period will be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover a period of 1500-2000 years between 500s. The second period, BC. 500-M.S. It’ll cover a period of 1000 years, called the Greek Mathematics period, between 500 years. The 3rd term, M.S. It will cover a 1200-year period from the 500’s until the start of calculus and will mainly cover European mathematics in the Hind, Islam and Renaissance era. The fourth semester will cover the classical mathematics era, referred to as the golden age of mathematics, dating from 1700-1900. The period we are residing in, dating back to the early 1900s, called age modern mathematics, would be the fifth period. I will endeavour to provide details about the development of mathematics for the reason that period, contributing mathematicians, the area of mathematics in social life and the basic options that come with mathematics in that period.

We will start the first semester with Egyptian mathematics. Written documents about ancient Egyptian mathematics and generally Egyptian history – I don’t mean the remains of archaeological works – are almost nonexistent. There are two significant reasons for this. The first is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason is the 3 big fires of the Alexandria libraries, the last of the fires happened throughout the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus could be the leaves of a reddish, reed type plant growing in the Nile delta, typically 15-25 meters long and 30-50 inches wide. These leaves were used to write text instead of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are based on the word papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it is flaky as a result of moisture, heat and similar reasons. Currently, two papyrus related to mathematics appear to possess been hidden under exceptional circumstances. The main sources of our understanding of Egyptian mathematics are both of these papyri. The very first of these papyrus is just a 6-meter long and 35-cm wide papyrus called the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is a copy written by a “mathematician” named Ahmes in the 1650s. This papyrus was bought by the Irish antiquarian H. Rhind in the 1850s, now in the British museum. This papyrus is a book written to show math. In the introduction part, after having a few exercises given to teach operations with fractional numbers, 87 questions are given with their solutions. They’re the type of questions people can encounter in lifestyle, such as for example sharing account, interest calculation, or finding the area of ​​some geometric shapes. That is pretty much our 8th grade mathematics. The second papyrus, called the Moscow papyrus and now in the Moscow museum, can be BC. It is a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the kind of questions in the Ahmes papyrus, aside from the two. Are you aware that other two questions, one is the calculation of the quantity and part of ​​the surface of the sphere part cut by way of a plane. The other could be the question of finding the volume of a pyramid cut with a plane. Both questions were solved correctly. Those two questions are accepted since the pinnacle of Egyptian mathematics. The Egyptians realized that the region of ​​the circle was proportional to its diameter and found the amount of pi to be 4x (8/9) squared, ie 256/81 = 3.16. It is understood that Egyptian mathematics has remained as of this level for 2000 years and has not made any significant progress.

B.C. 600s are the years once the Persians started to dominate the center east. B.C. By the 550s, Persians are the only real rulers of the whole middle east, including Anatolia and Egypt. The Persians organize three trips to Greece between 500-480 BC; They captured Athens in 480, but burned it, annually later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date which was accepted as the beginning of Greek civilization. This date is the beginning of a very bright period in science, art and literature. Greek mathematics actually started sooner than this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are considered to be the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he visited Egypt, stayed there for a while and learned geometry in Egypt. Whilst in Egypt, it’s described in books where he calculates the height of the truly amazing pyramid by measuring the size of the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to along the present shadow. After returning to Tales Milet, he taught them geometry by forming friends around him to teach what he learned. It is assumed that abstract proof centered on reasoning, which will be not predicated on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is recognized as the initial philosopher in human history. He came to be on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for a time, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully to Babylon by capturing the Persians through the occupation of Egypt by the Persians. it is known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after returning to Samos, he created a school and tried to teach the people he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the city of Crotone, where he created a semi-mystical-semi-scientific, cult-like school. The senior people of this school called “mathematics” live together and they’re connected to each other with oath. The 2nd group contains students attending school. Pythagoras school is founded on number cult. According for them, everything can be reduced to numbers; It posseses an unusually perfect harmony among numbers, and harmony is really a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as 1,2,3,…; and kes, ¾,… will be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem called the Pythagorean theorem (the square of the right sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a strong crisis. The discovery of irrational numbers is the very first major crisis of mathematics. Many of the members of the Pythagorean school were massacred with a raid led with a big cyber named Cylon. Pythagoras saved his life, but after a few years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As can be understood from these records, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.

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